386 
More generally, the complete primitive of the partial differential equa- 
tion in three independent variables 
1 1 1 
ate: 
x y 8 
D = ee ee pe aia a 
am pm ( 1 -a+tfP ie 
is 
Similarly, the integral of the partial differential equation 
1 1 1 1 
mt pe Than? Pay} 
\da*} dy? 
in the form of a complete primitive, is 
x y? ay “vw ey 
4 
B= yt ee 
Dai «tc D(a Ja) Renan oleate 
and the solution of 
1 1 1 Bhs 
@w \m i @yw \m 2 Cy \r 
dat dy? de 
is 
Z 2 2 yp. 
v= ee et Sse Ky 
2am 26") 2 een) 7 4 Zi 
So, again, the complete primitive of the partial differential equation 
1 1 1 ¢ 
ym tg gm Re 
is 
1 
as A rE TESTS 
Qo? 26" OG ag Bp. tous 
(5.) It may be interesting to compare for a particular case the solution 
in the form of a complete primitive with the solution in the form of a 
general primitive. Thus let us take the equation 
d*z a2 as 
r+ 28+¢=—_ +2 ——~ 4 —_-= 
ic i es dudy * dy ie 
